Two Nontrivial Weak Solutions for the Dirichlet Problem on the Sierpiński Gasket

Stancu‐Dumitru, Denisa

doi:10.1017/s000497271100298x

Cited by 7 publications

(2 citation statements)

References 12 publications

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“…Hua and Zhenya studied a semilinear PDE on self-similar fractal sets in [17] and a nonlinear PDE on self similar fractals in [34]. In [24], Denisa proved the existence of at least two nontrivial weak solutions for a Dirichlet problem involving the Laplacian on the Sierpiński gasket using the Ekeland variational principle and the critical point theory and in [25] studied the problem −∆u(x) + g(u(x)) = λf (u(x)), for x ∈ S \ S 0 u(x) = 0, for x ∈ S 0 . using variational method, she showed multiplicity of weak solutions for the problem.…”

Section: Introductionmentioning

confidence: 99%

A System of p-Laplacian Equations on the Sierpinski Gasket

Sahu¹,

Priyadarshi²

2018

Preprint

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In this paper we study a system of boundary value problems involving weak p-Laplacian on the Sierpiński gasket in R 2 . Parameters λ, γ, α, β are real and 1 < q < p < α + β. Functions a, b, h : S → R are suitably chosen. For p > 1 we show the existence of at least two nontrivial weak solutions to the system of equations for some (λ,for all (φ 1 , φ 2 ) ∈ dom 0 (E p ) × dom 0 (E p ), then we will call (u, v) to be a weak solution of (1.1). Differential equation on fractal domains has been of great interest for researcher for past few decades. We will go back in time line and give a brief review of literature survey. In [18,19,26,12], Laplacian is defined

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Section: Introductionmentioning

confidence: 99%

A System of p-Laplacian Equations on the Sierpinski Gasket

Sahu¹,

Priyadarshi²

2018

Preprint

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“…We refer to [40] existence of one non-zero strong solution for elliptic equations defined on the Sierpiński gasket. Moreover, in [45], author studied the following Dirichlet problem involving the weak Laplacian on the Sierpiński gasket…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

Alrikabi¹,

Afrouzi²,

Alimohammady³

2018

HJMS

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In this paper, we establish the existence and multiplicity results of solutions for parametric quasi-linear systems of the gradient-type on the Sierpiński gasket is proved. Our technical approach is based on variational methods and critical points theory and on certain analytic and geometrical properties of the Sierpiński fractal. Indeed, using a consequence of the local minimum theorem due to Bonanno, the Palais-Smale condition cut off upper at r, and the Palais-Smale condition for the Euler functional we investigate the existence of one and two solutions for our problem under algebraic conditions on the nonlinear part. Moreover by applying a different three critical point theorem due to Bonanno and Marano we guarantee the existence of third solution for our problem.

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A System of p-Laplacian Equations on the Sierpiński Gasket

Sahu

Priyadarshi

2021

Mediterr. J. Math.

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Two Nontrivial Weak Solutions for the Dirichlet Problem on the Sierpiński Gasket

Cited by 7 publications

References 12 publications

A System of p-Laplacian Equations on the Sierpinski Gasket

A System of p-Laplacian Equations on the Sierpinski Gasket

Existence and multiplicity of weak solutions for gradient-type systems wıth oscillatory nonlinearities on the sierpinski gasket

A System of p-Laplacian Equations on the Sierpiński Gasket

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